Problem 3: Calculate the maximum shear stress in the following beam section due to an internal shear force of V=150 kN. 200 mm 40 mm V = 150 kN 200 mm 40 mm
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- A U-shaped cross section of constant thickness is shown in the figure. Derive the following formula for the distance e from the center of the semicircle to the shear center. Also, plot a graph showing how the distance e (expressed as the non dimensional ratio e/r varies as a function of the ratio b/r. (Let b/r range from 0 to 2.)Calculate the shear stresses at point A in the adjacent T-beam.F(maks)= 200 kNA uniform wind load of q = 0.2 kN/m? acts on the billboard with dimensions of b = 1.5 m and a = 1 m. The allowable normal stress is oalow = 140 MPa, c = 0.5 m for the circular cross section panel pole. Draw the shear force, bending moment and torsional moment diagrams for the panel pole. a) Calculate the cross-section diameter d, using the maximum shear stress (Tresca) criterion. b) Calculate the cross-section diameter d, using the maximum distortional energy (von Mises) criterion. SOLUTION kesit
- 3 For the beam shown, find the reactions at the supports and plot the shear-force and bending-moment diagrams. V = 9 kN, V2 = 9 kN, V3 = 200 mm, and V4 = 1100 mm. ATAT-V3 Provide values at all key points shown in the given shear-force and bending-moment diagrams. X (mm) B A = B = C = D = E= F= P = Q = E * KN * KN * KN × KN KN x KN ✩ kN.mm *kN.mm D 0.00 Reaction force R₁ (left) = In the shear-force and bending-moment diagrams given, +V 0.00 X (mm) 6.3 kN and reaction force R2 (right) = P 11.7 kN. Q 0.00The simply supported beam is subjected to the force F = 700 N and the uniform distributed load with intensity w = 150 N/m. Draw the shear force and bending moment diagrams (in your homework documentation) and determine the equations for V(r) and M(x). Take a = 0 at point A. 19 F a Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 5.2 m 2.6 m 3.12 m Support Reactions The reaction at A is N. The reaction at D is N. Shear Force and Bending Moment Equations In section AB: V(x)= N and M(x)= N-m. In section BC: v(x)- N and M(x)= N-m. In section CD: V(x)- N and M(x)= N-m. A1. Calculate reactions at the external supports. 2. Draw the free body diagram. 3. Build the diagrams if shear force and bending moment. (use the section method) 4. Find the diameter of section of the beam. 5. Calculate the maximum Tangential Stress and show the corresponding section. 6. Draw the stress distribution diagram in the most dangerous section of the beam. a (m) 4 b (m) | P (kN) q (kN/m) 1 80 8 A D-? [G] - 100 MPa a q B b P
- Draw diagrams of shear force and bending moment for beam and loading shown. Calculate the maximum tensile and compressive stresses in the beam. X=407 N/m Y=2.21 m Z=51,4 mm1. Compute the maximum shear stress and maximum flexural stress of the beam shown in the figure. 20 ΚN 2 m 200 mm 25 mm 150 mm 5 KN/m 50 mm 15 KN/m 100 mm 5 KN/m 300mm 1.5 m 3.5 mFind the max shear stress in bending in the cross section below if Vmax = 10 kips. 10" Flange 2" Web 2" 8" Flange 2" 10" • Identify where in the cross section the max shear will occur. Determine the thickness of the cross-section at the location you wish to find shear stress. • Calculate the Ix for the shape (assume bending in the x with most basic beams). • Calculate Q by dividing the section into two pieces at the point you want shear stress. Select one of the pieces (either will work), I picked the top piece. Use the Shear Stress equation to determine the requested stress. Compare you answer: Max shear stress = at the center of the cross section.
- Consider the beam in (Figure 1). Take that M = 32 kN-m and P = 12 kN. Determine the normal force, shear force, and moment at point C. Follow the sign convention. igure M A с 1.5 m 1.5 m-1.5 m-1.5 m- B 1 of 1 ▼ Part A Determine the normal force at point C. Express your answer to three significant figures and include the appropriate units. No = Submit Part B Submit Part C ■μÀ HA Value Vc = Value Mc = Determine the shear force at point C. Express your answer to three significant figures and include the appropriate units. Submit Request Answer | MA 3 Request Answer HA Value Units Determine the moment at point C. Express your answer to three significant figures and include the appropriate units. Roquoot Anouor Units www. ? B Units ? ?QUESTION 3 If the allowable bending stresses for a beam in one application is 6 kip/in2 in tension. The cross-section of the beam is W8 x 40. If the beam is 10 foot long and simply supported and has a concentrated load applied at x = 3 ft as shown below. • Generate the shear force and bending moment diagram in terms of P; • Based on the allowable maximum bending moment you just obtained above, calculate/ input the mazimm allowable value of the load P: please, pay attention to units, and calculate your answer to 1 decimal place.. 3 ft 7 ft kip.3. For the structure carrying a uniform load of 4 kN/ m, compute the internal axial force, shear force, and Answer: Vc = 2 kN, Mc = 4 kNm, Nc = 24 kN bending moment at point C in the beam. 4 kN/ m |C B 3 m 2 m -2 m 2 m